The "primkl" command prints out the list of all the P_{gamma,nu} for
all pairs (gamma,nu) in the block, where gamma is "primitive"
w.r.t. nu, and gamma <= nu in the Bruhat order. "Primitive" means
that length(gamma) <= length(nu), and every descent for nu is
either a descent for gamma or type II imaginary ascent for gamma. A
consequence is that this list is guaranteed to contain all the
distinct k-l-v polynomials which occur.
We use the numbering of the elements in the block to represent gamma
and nu. To give meaning to these numbers, use the "block" command; that
will relate the various nu to fundamental representations, say, in terms of
Cayley transforms and cross-actions.
The polynomials are listed by gamma, and then for each gamma by
nu. The first line for gamma = 246 (say) looks something like
246: 28: q^2+1
This means that P_{28,246} = q^2 + 1. Each successive line for gamma
= 246 looks like
66: q^2+q+1
This means that P_{66,246} = q^2 + q + 1.
The last line of the file gives the total number of Bruhat-comparable
primitive pairs, the number of these for which the polynomial is zero,
and the number of primitive pairs that are incomparable in the Bruhat
order.
There is a blank line between distinct values of gamma in the output
file. The total number of lines in the output file is therefore
(#{Bruhat-comparable primitive pairs}) + (block size=#{gamma}) + 4